A Brief View upon Carnot Cycle and Gas Power Cycles

(written by: Willy Yanto Wijaya)

In thermodynamics, two most exciting and important cycles are Power Cycles and Refrigeration Cycles. Simply say, power cycles are thermodynamic cycles that convert other energy (usually heat) into work (power output). On the other hand, refrigeration cycles are thermodynamic cycles that utilize work (power input) to extract heat from one reservoir (lower temperature) and transfer it to the other reservoir (high temperature). Based on the phase of working fluid, thermodynamic cycles can also be categorized as gas cycles and vapor cycles. In this writing, we will focus particularly on the gas power cycle and its connection with the Carnot cycle.

Carnot cycle is an ideal thermodynamic cycle which comprises of no irreversibility. Therefore, heat engine (device operated on power cycle) based on the Carnot power cycle will have the theoretical maximum efficiency. However, even with no irreversibility, the efficiency of Carnot cycle will never be 100%. The reason is that in order to complete a full cycle, some heat has to be dissipated to the reservoir. This is actually the essence of the second law of thermodynamics. Then how is the maximum possible efficiency of Carnot cycle? Based on the Kelvin-Planck statement and thermodynamic temperature scale, the efficiency of Carnot cycle depends only upon the reservoirs temperatures (Effth,carnot = 1 – (TL/TH)).

As a matter of fact, Carnot cycle is composed of four processes:

1-2: isothermal heat addition

2-3: isentropic (adiabatic + internally reversible) expansion

3-4: isothermal heat rejection

4-1: isentropic compression.

These processes can be described with the P-V and T-S diagrams as shown in Fig.1. However, in reality, the process (1-2) and (3-4) (isothermal heat addition and rejection) are difficult to be realized (it will require very large heat exchangers and take a long time). Therefore, Carnot cycle is not suitable and realistic as an ideal model for the actual power cycles.

The actual power cycles are apparently quite complex and thus some assumptions are made to simplify them without losing the essence. Air standard assumptions are also utilized in the ideal gas power cycles. Here, we shall pick two samples of ideal gas power cycles (Otto and diesel cycles), and briefly discuss them with comparison to the Carnot cycle.

Otto cycle is the ideal model for the spark-ignition engine. This air-standard Otto cycle is composed of four processes:

1-2: isentropic compression

2-3: isochoric heat addition

3-4: isentropic expansion

4-1: isochoric heat rejection,

which can be described with the P-V and T-S diagrams (as shown in Fig.2). In this ideal Otto cycle (also Diesel cycle), there is no internal irreversibility (such as: flow friction, etc) however they may still have external irreversibility (such as heat transfer through a finite temperature difference). This is the reason why the thermal efficiencies of these ideal power cycles are lower than the thermal efficiency of Carnot cycle. From the above-mentioned four processes, we can see that the “heat addition and rejection” processes in Otto cycle are not isothermal (as in the Carnot cycle), and therefore entropy will be generated through this heat transfer processes.

The same thing happens in Diesel cycle as well. Diesel cycle is the ideal cycle for the compression-ignition engines, which is composed of following processes:

1-2: isentropic compression

2-3: isobaric heat addition

3-4: isentropic expansion

4-1: isochoric heat rejection,

and described by the P-V and T-S diagrams (Fig.3). Indeed there is no internal irreversibility in this Diesel power cycle, however some external irreversibility still occurs i.e. in the isobaric heating (2-3) and isochoric cooling (1-4) above. Therefore, the thermal efficiency of Diesel engine will be also lower than that of Carnot cycle. It is interesting to note that the main difference between the ideal Diesel cycle and Otto cycle is just the heat addition process (2-3).

Further, many other power cycles, either gas or vapor cycles, have been developed. These power cycles are certainly somewhat idealization of the actual power cycles, however they still serve as a useful and more suitable model for the actual implementation compared with the Carnot cycle. Therefore, we can conclude that the differences these ideal power cycles possess from the Carnot cycle are substantially caused by their practical-oriented implementation for different specific real-system applications respectively.

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2 Responses to A Brief View upon Carnot Cycle and Gas Power Cycles

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